Radio-frequency band-pass filter wherein magic-tee arms are coupled to cavities and resonators

ABSTRACT

A radiofrequency band-pass filter having a flat amplitude response and a substantially constant group delay characteristic in the passband, these being obtained by the integrated combination of a magic-tee terminated with reflecting cavities, and input and output transmission resonators, the integration of the components being essential to achievement of the above characteristics. For the same complexity this filter has a higher stop-band attenuation and smaller midband insertion loss than a conventional nonintegrated filter/phase-equalizer combination.

States Patent Inventor Appl. No.

Filed Patented Assignee Priority Larry Joseph Stagg Harrow Weald, England 834,687 June 19, 1969 Aug. 31, 1971 Companies Limited London, England June 20, 1968 Great Britain 29577/68 RIO-FREQUENCY BAND-PASS FILTER WHEREIN MAGIC-TEE ARMS ARE COUPLED T0 V [56] References Cited UNITED STATES PATENTS 2,629,015 2/1953 Reed 333/73 (W) 2,649,576 8/1953 Lewis 333/73 (W) 3,422,380 1/1969 Kuroda et a1. 333/73 X 3,423,698 1/1969 Wilson 333/73 X Primary Examiner-Herman Karl Saalbach Assistant Examiner-Paul L. Gensler Anorney- Kirschstein, Kirschstein, Ottinger & Frank CAVITIES AND RESONATORS 3 Claims, 7 Drawing Figs.

US. (I 333/73 W, 333/ l 1 Hm. 1101p 1/20 Field ofSearch 333/73, 73 w, 10, 1 1

PATENTEB M831 am 3,602

" sum 3 0F 3 'NVENTOR LARRY I 515:

AT TORNEYS RADIO-FREQUENCY BAND-PASSFILTER WHEREIN MAGIC-TEE ARMs ARE COUPLED T CAVITIES AN RESONATORS I The present invention relates to radiofrequency filters and particularly to such filters having a band-pass characteristic and employing waveguide components.

Conventional radiofrequency (r.f.) filters commonly exhibit a characteristic of phase-shift I against frequency w which is nonlinear with the result that the rate of change of phase-shift with frequency is not constant, that is, that the group-delay,

d bldw, of the filter is not constant. Some types of modulated signals within the passband can therefore be distorted by the filter. This difficulty has been overcome by following the filter with a phase-equalizer which has no significant filtering characteristic, that is, it has an all-pass characteristic, but which has a group-delay characteristic complementary to that of the filter in the passband.

The combination thus provides a band-pass characteristic within which the group-delay is constant. It is to be noted that the filter and equalizer should have no interaction, that is each should play its part quite independently of the other.

According to one aspect of the present invention a radiofrequency band-pass filter comprises a hybrid junction waveguide component having a first pair of arms in conjugate relation, these arms being terminated by cavities resonant at a frequency approximating to the center frequency of the filter and having different loaded Q factors, the other pair of arms being coupled to respective waveguide resonators resonant at said center frequency, and the lengths of waveguide between said waveguide resonators and said cavities being such as to give the filter an overall band-pass characteristic with substantially constant group-delay in the passband.

According to another aspect of the invention, a method of manufacturing a nonminimum-phase waveguide band-pass filter comprises the steps of specifying amplitude and phase characteristics of a low-pass transfer function, determining the lumped-circuit component values for a low-pass network, (which includes a lattice) exhibiting said transfer function, transforming the low-pass network to a band-pass network of required frequency and bandwidth and realizing the band-pass network by waveguide components including a waveguide hybrid junction.

A radiofrequency band-pass filter in accordance with the invention will now be described, by way of example, with reference to the accompanying drawings, of which:

FIGS. 1 and 2 show a plan and partial end view of the filter 2 (coupling flanges not being shown);

FIGS. 3 and 4 show plan and end view of a magic tee on which the filter centers;

FIG. 5 is a prototype low-pass network illustrating the derivation of the filter;

FIG. 6 is a band-pass network obtained by transformation from the network of FIG. 5;

and FIG. 7 shows a pole-zero diagram of the characteristic function for a low-pass amplitude response.

Referring to the drawings, FIGS. 1 and 2 show a self-equalized filter for operation at a center frequency of 6153.5 MHz. and over a bandwidth of 30 MHz. The filter is constructed in waveguide No. 14 (WR-l37) and comprises colinear input and output arms I and '2 coupled to a magic-tee 3 to the other ports of which are coupled an H-arm resonant reflecting cavity 4 and an E-arm'resonant reflecting cavity 5 shown in FIG. 2.

The H-arm extends from the narrow face of the main (1, 2-) guide and the E arm extends fromthe broad face of the main guide in known manner.

The magic-tee 3 is shown more particularly in FIGS. 3 and 4. This comprises a block of brass 6, or preferably other metal having lower temperature coefficient of expansion, and internally plated with high conductivity metal..in which there are two colinear ports, an Earm port shown in FIG. 3 and an H- arm port shown in FIG. 4. A flange 7 provides a coupling for the I-I-arm port, while the input and output arms, and the E- arm reflecting cavity 5 have flanges which are screwed on to the respective faces of the block 6.

The I-I-arm is matched by a post 11 which is mounted on the centerline of the l-I-arm on the broad face of the main (1, 2) guide projecting towards the E-arm. The post 11 has a diameter of 0.156 inches, a length of 0.900 inches and its center is positioned 0.531 inches from the narrow face of the main (1, 2) guide remote from the I-I-arm. These dimensions are suitable for center frequencies to in the lower 6 GI-Iz. band.

The E-arm is matched by an iris 12 extending across the E- arm for a distance 0.440 inches measured from the narrow side of the guide adjacent the I-I-arm. The thickness of the iris is 0.036 inches and it is spaced 0.265 inches from the upper broad face of the main'( 1, 2) guide as shown in FIG. 4.

' The H-arm reflecting cavity 4 is coupled by two posts 13 of diameter 0.0475 inches with center spaced at 1.270 inches from the short-circuited closed end of the cavity. The E-arm reflecting cavity 5' is coupled by two posts 14 of diameter 0.0705 inches diameter with centers spaced at 1.295 inches fromthe short-circuited closed end of the cavity.

It is noted that the different coupling post diameters establish different Q factors for the two resonant cavities 4 and 5.

Each of the input and output arms 1 and 2 of the filter includes transmission resonators which in form resemble those of a conventional filter.

The resonators in each of the colinear arms are coupled by four rows of posts, all of the rows being arranged symmetrically about-the centerline of the broad face of the guide, as shown in FIG. 1. Numbering the rows from the magic-tee outwards, the first. row (15) comprises two posts of diameter 0.079' inches and center spacing 0.350 inches, the second row comprises three posts of diameter 0.138 inches and of center spacing 0.280 inches, the third row comprises three posts of diameter 0.122 inches and of center spacing 0.280 inches, and the fourth row comprises two posts of diameter 0.0505 inches and of center spacing 0.350 inches. The spacing between the first and second row (centers) is 1.338 inches, between the second and third row is 1.406 inches and between the third and fourth row is 1.306 inches. The transmission resonators of the input and output arms 1 and 2 are identical and symmetrical about the magic-tee. The center spacing of the two first rows (15) of posts, that is, those immediately adjacent the magic-tee, is 1.70 inches. The length of guide between the I-I-arm reflecting cavity 4 and the magic-tee is specified by the distance between the centerline of the coupling posts 13 and the adjacent internal narrow face of the main (1, 2) guide. This distance is 1.47 inches. In the case of the E-arm reflecting cavity 5 the length of guide is specified by centerline distance between the centerline of the coupling posts 14 and the near surface of the matching iris 12. This distance is 0.75 inches.

If the self-equalizing filter were simply a combination of a conventional filter, similar to the transmission resonator arms 1 and 2 and an all-pass phase-equalizing component similar to the magic-tee with the reflecting cavities, then the cavities 4 and 5 would be of equal Q value and both filter and all-pass component would be separately and fully matched. Also, the line lengths between the reflecting cavities 4 and 5 and the transmission resonators would be of no consequence. In the present case, on the contrary, the dimensions between the first row of posts 15 in each transmission resonator and the coupling posts 13 and 14 of the two reflecting cavities are critical. In addition as has been noted, the reflecting cavities 4 and 5 are of different Q values.

The significant dimensions of the self-equalizing filter are achieved on the basis of the following theory.

FIG. 5 shows a low-pass lattice network which can be transformed to the band-pass network of FIG. 6 by standard techniques.

Such a low-pass prototype circuit as FIG. 5, being a lattice network, is what is known as a nonminimum-phase network,

that is, one which has infinite attenuation poles at complex frequencies and which consequently provides a greater phase shift through the network than that through a comparable network having the same amplitude response. This fact causes the network to have phase and amplitude characteristics which may be varied independently. The low-pass network of FIG. 5 is first transformed to the band-pass network of FIG. 6 and this network is realized in the waveguide circuits of FIGS. 1 and 2. Amplitude and phase characteristics in accordance 1th the known requirements are specified for the low-pass prototype network and the component values detennined.

A transfer function for a lowpass response is assumed, having for the filter of this example, a Chebyshev amplitude ripple of magnitude according to the limit specified for the passband of the final filter. For other examples the filters might have different, for example, maximally flat amplitude responses. This function will be designated H(p), where p is the frequency operator j w, j is -l and w is angular frequency. H( p) may be defined by |H(p)l w/Pmax/P where P is the maximum the real p axis and the vertical axis the imaginary p axis on the same scale. The source and load impedance g, of FIG. 5 are normalized to a value of l ohm and the frequency is normalized to a cutoff value of w equal to l radian/sec. It will be appreciated that the vertical, imaginary p axis in FIG. 7 is in fact is a frequency transformation given by the Chebyshev cutoff frequencies f, and f and E=zF is the I-Iurwitz polynomial formed by the poles of K(p) transformed to the 2 plane. The computation steps involved in evaluating this equation are given in the reference.

The constant multiplier k is calculated for the Chebyshev filters by considering the maximum permissible ripple in the passband. For any filter the maximum ripple occurs at the cutoff frequency. For the low-pass prototype filter this frequency is given by p=jl and substituting this frequency into K(p) and comparing with the permissible ripple gives k. v V

In determining the function K(p) above, the position 0 of the pole on the real p axis was chosen by informed guessing. Following the derivation of the poles and zeros of H( p) on the basis of this guess the group delay 1' can then be determined. It can be shown that where a is the root of H(p) giving a zero on the real p axis, N is the number of zeroshere seven, 1' is the number of the conjugate pairs of zeros of H(p), and H( p) comprises the product of the quadratic factors (p +a,-p+b,) from i=1 to i=N-l/2.

From the above expression the group delay variation over the passband is checked and further values of 0 tried until a satisfactory variation is achieved.

Having now found the poles and the zeros of the characteristic function K(p), the original transfer function H(p) can be found from the expression relating H( p) and K( p). In fact it is not necessary to derive the actual expression of H(p) and the information which would appear in H( p) can be derived by the following method.

K(p) has been established broadly as pS/P, where p=jw and v S and P are even polynomials in p. From the relation |H(p)| a real frequency axis and the point p=jl on this axis is the cutoff angular frequency W,.. I

For the lossless circuit of FIG. 5, K( p) must be purely imaginary. It therefore consists of the ratio of even polynomials with an additional factor or divisor p. As a low-pass circuit it cannot have a pole of infinite attenuation at zero frequency and therefore the p is a factor and there is a zero of K(p) at zero frequency. All other zeros of K(p) Occur in conjugate pairs. There must therefore be an odd number of zeros and the present characteristic is accorded seven to be comparable with conventional filters.

The same number of poles will appear in the function K(p) and two of these are attributed to complex frequencies corresponding to values I 0 on the real p axis. It is the nonminimum-phase character of the low-pass network which produces these complex frequency poles. There is freedom to specify the value of 0 independently of the amplitude characteristic and this freedom provides a choice of group-delay characteristic.

The remaining five poles are attributed to infinite frequency conditions. I

In general, for a given passband amplitude response, the zeros of K(p) depend on the pole positions, and hence, if the complex pole positions are changed the zeros of K(p) aLso change. For an equal-ripple Chebyshev amplitude response, these zeros can be obtained by the method described in Section 3F of a paper On the design of filtbrs by synthesis by Saal, R., and Ulbrich E., IEEE Trans, 1958, CT-5, pp. 284327K(p) is given in terms ofthe pole I l+| K(p)| 2 it can easily be shown that It is known that, for a passive network, the zeros of a transfer function H(p) must lie in the left'hand half of the complex pplane. It is therefore required to extract from the expression (PpS)(P+pS) those roots which lie in the left-hand half of the p-plane. If H(p) were to be expressed as: (g-l-pu)(G+pU)/P, it so happens that the factors of (pi-p5) would be equal to (g+pu )(Gpup+pS) only, and changing the signs of roots so formed so as to make them lie in the lefthand half of the p-plane, the zeros of H(p) are obtained. The

\poles are the same as for K( p).

If the prototype network is considered initially as a lattice only, and of series and shunt arm impedances Z and 2, respectively, these are given as follows:

Because the circuit is symmetrical, the lattice impedances can be related to the open and short circuit impedances of half of an equivalent symmetrical network, that is, to half of the network shown in FIG. 5. If the lattice in that circuit is considered to have series inductances L and shunt capacitances C, it can be shown that the open-circuited half lattice is equivalent to a shunt capacitance of value C and the short-circuited half lattice is equivalent to a shunt inductance of value L.

The first two poles at w=-'== derived from H(p), are common to both open and short circuit impedances and these are removed, thus determining g and g;. The remainder of the half circuit is, for the short circuit case, a shunt capacitance which is g; and the shunt inductance L. In the open circuit case the remainder of the lattice is the capacitance g;, in parallel with the above shunt capacitance C, the total being initially I derived as, say, C and C being extracted by subtraction of g from C;,. L and C are g, and g,, respectively and thus all five components 3,, g g g and g are evaluated.

This derivation of the circuit component values from the open and short circuit impedances is standard procedure and it is only necessary to provide the two impedances and the poles of the transfer function to determine the network in the above form.

The element values of various prototypes aretabulated in Tables 1 to 3, together with their group delay variations for selected values of Q, the low-pass frequency variable normalized to the cutoff frequency. The prototype values are given,

not only for different amplitude passband ripples, but also for 5 difi'erent group delay variations. The group delay variations must be considered because, when the low-pass prototype is transformed to a band-pass filter, the achieved group delay varies, depending on the filter center-frequency and bandwidth and, in the case of a waveguide filter, on the guide wavelength variation with frequency. Therefore in order to obtain the required group delay characteristics, the most suitable prototype can be selected. 1

TABLE 1 l 5 Element Values and Group Delay Variation of 0.001 db Ripple Prototypes TABLE 2 Element Values and Grou Delay Variation of 0.01 db Rlppe Proto- 95 WP N=7 1 1 1 0. 7912 0. 7925 0. 7886 1.3778 1.3798 1,3792 1. 4671 1. 4950 1. 5148 1. 1284 1. 0874 1. 0540 0. 6154 0. 5441 0. 4840 5 5 Group delay, 1"

0.1 (lb Ripple Prototypes The group delay 'rof the band-pass network shown in F 6 is given in terms of the group delay 7' of the low-pass network by the following expression 1 I om m'f g( n+ (1) where )tg is the guide wavelength, 1, A A are the guide wavelengths at the center frequency and the edge frequencies of the band respectively, and c is the velocity of light.

in coupling the transmission resonators of FIG. 6 to the lattice resonators there is, in that lumped circuit, zero line length between the lattice and the other resonators. In the waveguide arrangement this is not possible and consequently some phase shift is effected by the coupling lines. By keeping the coupling lines in integral numbers of half-wavelengths this phase-shift can be ignored at the center frequency although not satisfactorily at frequencies at the edge of the band. The coupling lines may, however, be considered as resonators and the effect of them can therefore be incorporated in the resonators which they couple.

The equivalent resonator is given by where n is the number of half-wavelengths constituting the coupling line, and WA is the difference in the guide wavelengths at the extreme frequencies divided by the center frequency guide wavelength. The equivalent line resonator giving an element value g is best considered as being in two parts, one at each end of the coupling line. The value g'l2 is thus subtracted from the value g;, of the prototype. In the case of the reflecting cavities 4 and 5, each of these has a coupling line which is employed as both input and output for the cavity and consequently g is subtracted from the prototype lattice elements. 1

The design of the filter shown in FIGS. 1 and 2 will now be described. For this filter, the passband frequencies are 6138.5 MHz. to 6168.5 MHz. If A A, and A, are the guide wavelengths at f0 and the band'edge frequencies respectively, then their values are For a required, theoretical, passband amplitude ripple of 0.001 dB, the prototype values are given in Table 1 for the different group delay variations. These variations are calculated for the band-pass filter using Table l and Equation (1). For the above filter those calculations show that the 6=l.3 case has an almost flat group delay across the center of the passband and therefore the prototype values corresponding to this are selected. These values are g ,=0.5541 and The values of 3 g and g,, are adjusted to allow for the effect of the coupling lines are described above. For half-wave coupling lines on each side of lattice (n=l), Equation (2) gives Adjusted prototype values are g =g,,g =0.5248 For prototypes normalized to the load impedance and with an angular cutoff frequency of unity, the coupling impedances,

7 of end posts coupling from a cavity to a length of guide are lrn Z.. 29..

where g, is the prototype value of the coupled resonator. The coupling susceptances B/Y, are then given by Y K Z (4) For two cavities which are directly coupled, the coupling impedanceis Equation (3) is used to calculate the end coupling posts of the input and output sections of the filter, and the posts coupling the reflecting resonators on the magic-tee. As for conventional filters, Equation (5) is used for the other posts. Therefore for the example, from Equation (3) Similarly b o o .74

where B,,/Y,, and B,,/(, are the susceptance values for the posts coupling the reflecting resonators 4 and 5 From Equation (5) Therefore 8 Y,,=82. l 3 Similarly B /Y,,=55. l 9

In the above B/Y susceptance expressions for the various rows of coupling posts, the suffix of B indicates the number of the row from each end of the filter towards the magic-tee. The transmission cavity lengths are calculated from the 8/ Yo values as for conventional filters. The reflecting cavities are coupled by only one finite susceptance and therefore the electrical length of these is given by and -l 0- 1r c0t 0) The cavity lengths are corrected for the effective short circuit position of the posts in the same way as for conventional filters.

The post diameters are obtained from the required B/Yo values. The end posts of the input and output sections, which are adjacent to the magic-tee, are found in most cases to require a tuning adjustment to enable the filter to be tuned to a good return loss. To allow for the tuning, it was found to be satisfactory to increase these post diameters by a factor of 1.025 (i.e. 2% percent).

The remaining dimensions. to be determined, are the line lengths coupling the magic-tee.

lt is not practical to calculate the physical line lengths required for coupling the reflecting cavities 4 and 5 and the input and output anns 1 and 2 to the magic-tee, because of the complex nature of the junction. A test arrangement may be employed in which the line lengths coupling the cavities 4 and 5 to the magic-tee are adjustable as also is the position of post resonators in the input and output guides simulating the first transmission resonator posts in the actual input and output arms. This arrangement, when placed between matched loads is found, by checking the insertion loss, to give very narrow resonances due to the E-arm and the H-arm, the resonances occurring when the total effective line length between the main guide posts and the coupling posts of one or the other reflecting cavity is an integral number of half-wavelengths. The resonances due to the two arms occur independently and those due to one of the arms can be changed without affecting those due to the other one.

The line lengths should be those which give a resonance at f0 due to the equivalent series resonator and an antiresonance at f0 due to the equivalent shunt resonator.

When a correct setting of coupling line lengths has been measured, it is possible in some cases to reduce the lines by a further M4 by interchanging the cavities. The change of cavity and the change of line length each produce the dual of the lattice and thus leave it finally unchanged.

Spurious resonances are produced by the shunt resonator at frequencies symmetrically positioned about the center frequency. These spurious resonances cause a reduction in the stop-band attenuation at these frequencies, but their effect is reduced by reducing the coupling line lengths to a minimum. It is therefore desirable that the coupling lines should be of the minimum possible length. Having determined the minimum coupling line lengths in this way the filter of FIGS. 1 and 2 is constructed.

The midband insertion loss of this filter is 1.2 dB. The flatness of the passband response is indicated by 0. 1 dB points occurring at f0-l2 MHz. and fo+15 Ml-lz. while the 1.0 nanosecond group delay points occur at fo-lO MHz. and fo+l 2 MHz.

It may be seen that, superficially, the transmission resonators of arms 1 and 2 resemble a conventional filter while the magic-tee may be considered separately as a phase equalizer. However the advantages of the present invention are inherent in the integral nature of the design and are immediately lost when either the transmission resonators or the magic-tee and its reflecting cavities are designed in isolation as a filter or a phase equalizer respectively. This is most immediately apparent from the fact that the guide path length between the reflecting cavity resonators and the transmission resonators is critical.

The advantage of the filter of the invention designed as it is to have both constant amplitude and group delay in the passband, is an improved stopband rejection compared to conventional filter-plus-equalizer combinations of similar overall complexity. The use of this improved stopband response leads to a filter with fewer cavities for a particular required amplitude response, this in turn leading to an improved group delay characteristic.

lclaim:

l. A radiofrequency band-pass filter comprising a hybrid junction waveguide component having a first pair of arms in conjugate relation, these arms being terminated by cavities resonant at approximately the center frequency of the filter and having different loaded Q factors, the other pair of arms being coupled to respective input and output waveguide resonators resonant at said center frequency, the lengths of waveguide between said waveguide resonators and said cavities being an integral number of half-wavelengths such as to give the filter an overall band-pass characteristic with substantially constant group-delay in the passband.

2. A filter in accordance with claim 1, wherein said hybrid junction is a magic-tee, the conjugate arms being the E and H arms, and each of the colinear arms including a number of post-coupled resonators.

3. A filter in accordance with claim 2, wherein the nearest posts of said post-coupled resonators to the magic-tee are as near as is physically practicable. 

1. A radiofrequency band-pass filter comprising a hybrid junction waveguide component having a first pair of arms in conjugate relation, these arms being terminated by cavities resonant at approximately the center frequency of the filter and having different loaded Q factors, the other pair of arms being coupled to respective input and output waveguide resonators resonant at said center frequency, the lengths of waveguide between said waveguide resonators and said cavities being an integral number of half-wavelengths such as to give the filter an overall band-pass characteristic with substantially constant group-delay in the passband.
 2. A filter in accordance with claim 1, wherein said hybrid junction is a magic-tee, the conjugate arms being the E and H arms, and each of the colinear arms including a number of post-coupled resonators.
 3. A filter in accordance with claim 2, wherein the nearest posts of said post-coupled resonators to the magic-tee are as near as is physically practicable. 